• What is a phylogeny?
  • A model of evolutionary history
    
  • Speciation and extinction
    
  • Rates of evolution
    
  • (Maybe) absolute time

• But there are also special challenges to using phylogenetic trees to study the evolutionary history of traits

Let’s say that in your group of organisms, you believe that arboreality is associated with lower visual acuity.

Let’s say that in your group of organisms, you believe that arboreality is associated with lower visual acuity.

arboreality <- c(.1, .2, .3, .4, .5, .6, .7, .8)
vis_ac <- c(1, .8, .6, .4, .35, .3, .25, .2)
plot(arboreality, vis_ac)

What is wrong with what we have done?

arboreality <- c(.1, .2, .3, .4, .5, .6, .7, .8)
vis_ac <- c(1, .8, .6, .4, .35, .3, .25, .2)
plot(arboreality, vis_ac)

What is wrong with what we have done?

arboreality <- c(.1, .2, .3, .4, .5, .6, .7, .8)
vis_ac <- c(1, .8, .6, .4, .35, .3, .25, .2)
plot(arboreality, vis_ac)

These are not independent datapoints!

What is the problem with what we’ve done?

Felsenstein Phylogenies and the Comparative Method, 1985

These are not independent datapoints!

Does this mean we simply can’t make these comparsions?

Does this mean we simply can’t make these comparsions?

No! But we must account for the effect of shared heritage.

• Based on the random movement of particles in fluid

• The idea is that sucessive movements are independent of each other.

• Under this model, traits evolve due to a continuous random walk.

• The difference (contrast) between the traits possessed by any two tips on the tree will be normally distributed. The mean of the normal will be 0, and the variance will be proportional to the time since common ancestor.

x <- seq(-4, 4, length=100)
norms <- dnorm(x, sd = 1)
plot(norms)

steps <- 0:50  
var <- 0.01
x <- rnorm(n = length(steps) - 1, sd = sqrt(var))
x <- c(0, cumsum(x))
plot(steps, x, type = "line")

## Warning in plot.xy(xy, type, ...): plot type 'line' will be truncated to
## first character

steps <- 0:50  
var <- 0.01
n_sims <- 50
sim_mat <- matrix(0, n_sims, length(steps))


for (i in 1:n_sims) {
  sim_mat[i, ] <- c(0, cumsum(rnorm(n = length(steps) - 1, sd = sqrt(var))))
}

plot(steps, sim_mat[1, ], type = "line", ylim = c(2, -2)) #when you scale var, you may need to adjust the axis!

## Warning in plot.xy(xy, type, ...): plot type 'line' will be truncated to
## first character

for (i in 1:n_sims) {
  lines(steps, sim_mat[i, ])
}

1, 2, 3, 4 are not independent. But the difference between 1 & 2 is independent of the difference between 3 & 4.

Contrasts usually standardized by the variance

library(phytools)

## Loading required package: ape

## Loading required package: maps

tree <- pbtree(n=20)
x <- fastBM(tree, sig2 = var, internal = TRUE)
x

##          t19          t20           t3           t4           t8 
##  0.009223212 -0.070437080  0.124401752  0.088344109 -0.033095364 
##           t9          t15          t16          t14           t5 
##  0.117956632  0.111424898  0.149738231 -0.085196710 -0.018092583 
##           t6           t1          t12          t17          t18 
## -0.026754123 -0.045039932 -0.181212061 -0.102056619 -0.080236832 
##          t13           t2           t7          t10          t11 
## -0.131576134  0.008612053  0.060299042 -0.011597639 -0.049667398 
##           21           22           23           24           25 
##  0.000000000 -0.070681148 -0.032780087 -0.015801379  0.013007371 
##           26           27           28           29           30 
##  0.033602870  0.031192369  0.079338202  0.011105571  0.128412717 
##           31           32           33           34           35 
##  0.131956955  0.037707082 -0.181939928 -0.170017030 -0.144654497 
##           36           37           38           39 
## -0.161316965  0.043964325  0.023988578  0.037729690

phenogram(tree, x)

x <- fastBM(tree, sig2 = var, internal = FALSE)
contrasts <- pic(x, tree, scaled=FALSE)
contrasts

##            21            22            23            24            25 
## -0.2115216923 -0.0844633705  0.0168993895 -0.1570753861 -0.0960292860 
##            26            27            28            29            30 
##  0.1875301617 -0.1159904336  0.1149664747 -0.1915242398 -0.0139271755 
##            31            32            33            34            35 
##  0.0246090861 -0.0267121758 -0.1799226895  0.0383846328  0.0423184074 
##            36            37            38            39 
##  0.0678331583 -0.1436154218  0.0604193728 -0.0004905934

plot(tree)
nodelabels(contrasts)

important_environmental_factor <- seq(from = 1, to = 19, by = 1)
plot(contrasts, important_environmental_factor)

• Ancestral state estimation
• Models, and model assumptions

Phylogenetic independent contrasts assume we can estimate the value of the trait possessed by an ancestor through Brownian motion

• But we’ve already seen ancestral state estimation
  • Recall the AND/OR rule discussions from day one
    
  • Conditional probabilities - What is the likelihood of a state at the tips given the state at the nodes
    
  • Ancestral state reconstruction allows us to apply this logic to external traits

• Ancestral state reconstruction can vary in its complexity
  • The first applications came from parsimony (Swofford and Maddison 1987)

tree_20 <- pbtree(n=20)
trait <- fastBM(tree_20)
phenogram(tree_20, trait)

anc_states <-anc.ML(tree_20, trait)
plotBranchbyTrait(tree_20, trait)

tree_20$tip.states <- trait
tree_20$node.labels <- anc_states$ace
write.tree(tree_20, file = "annotated.tre")

We’re going back to RevBayes for this.

These methods all assume the tree you tell it is the true tree

These methods all assume the tree you tell it is the true tree

These methods all assume the tree you tell it is the true tree

These methods all assume the tree you tell it is the true tree

These methods all assume the tree you tell it is the true tree

These methods all assume the tree you tell it is the true tree

• Use multiple estimates from different points in tree space

• BiSSE
• BAMM